Question

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log x, and log y.
log x^2/y^4

Answer 1

`\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} ~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log\left( \cfrac{x^2}{y^4} \right)\implies \log(x^2)-\log(y^4)\implies 2\log(x)-4\log(y)`